Rolling virtual wheel spindle calibration

ABSTRACT

A vehicle wheel alignment system and method is provided for performing a rolling wheel axis of rotation and wheel spindle point calculation every time an alignment is performed. Embodiments include an aligner having a target fixedly attachable to a wheel of the vehicle; a camera for viewing the target and capturing image data of the target; and a data processor. The data processor receives the image data from the camera, and determines a vector pointing from the target origin to a wheel spindle point based on the captured target image data, when the vehicle is rolled while the wheel is on a substantially flat surface such that the wheel and target rotate a number of degrees. The data processor is further adapted to calculate an alignment parameter for the vehicle based at least in part on the wheel axis of rotation and the coordinates of the wheel spindle point.

FIELD

Embodiments relate generally to systems and methods of automotive wheelalignment. The present subject matter has particular applicability todetermining true values of wheel alignment parameters such as camber andtoe angles for a vehicle when using an image aligner having targetsattached to the vehicle wheels, and cameras to image the targets.

BACKGROUND

Machine vision vehicle alignment systems using movable cameras andtargets attached to vehicle wheels, also known as “image aligners,” arewell known. The targets are viewed by the cameras such that image dataobtained for a prescribed alignment process can be used to calculatevehicle alignment angles for display through a user interface, usually acomputer monitor. Early system implementations included rigid beams thatconnected the cameras so that their position and orientation withrespect to each other could be determined and be relied upon asunchanging. Later system implementations were introduced comprising theuse of cameras not rigidly connected to each other, but using a separatecamera/target system to continuously calibrate the position of onevehicle mounted target viewing camera to another. This type of system isdescribed in U.S. Pat. Nos. 5,535,522; 6,931,340; 6,959,253; and6,968,282, all of which are hereby incorporated by reference herein intheir entirety. An example of a vehicle wheel aligner using such imageprocessing is the Visualiner 3D or “V3D”, commercially available fromJohn Bean Company, Conway, Ark., a division of Snap-on Incorporated.

In order to be able to accurately measure wheel alignment angles for avehicle using an image aligner, the wheel axis of rotation around whichthe target rotates must be measured, and the coordinates of the virtualwheel spindle point through which the vector passes must be determined.

The conventional method for calibrating the combined system of a targetand clamp involves lifting the vehicle off the supporting surface (e.g.,the shop floor or an alignment rack) so the wheels with targets mountedare able to rotate freely. The wheels are then rotated to predeterminedpositions to enable determination of the vector defining the wheel axisof rotation. Since the target origin traverses a circular arc, thecoordinates of the center of the circle are computed from points on thecircumference of the arc. The center of the circle is on the wheel axisof rotation and is referred to as the virtual wheel spindle point. Thevirtual wheel spindle point is projected along the wheel spindle axis tothe plane of the wheel rim. The projected point is the wheel spindlepoint. This is illustrated in FIG. 1, wherein a vehicle 100 on whosewheel a clamp 110 carrying a target 120 is mounted. Coordinates are in atarget coordinate system. The axis of rotation vector 130 passes throughthe wheel spindle point 140 and virtual wheel spindle point 150. Thetarget centroid is offset from the virtual wheel spindle point 150.

Typical wheel clamp and target assemblies are manufactured so thatcalibration processes do not have to be repeated every time a clamp isremoved from a wheel. Conventional target assemblies commonly employself-centering wheel clamps for this purpose. Clamp mounting errors arecompensated for by a well-known rolling runout calculation.

A calibration procedure for the system of target and self-centeringclamp is typically performed by a technician when an aligner is firstset up, using custom calibration equipment. It must be performedthereafter whenever a new target is introduced to the system; forexample, when a target is replaced. Disadvantageously, the end user mustwait for a service technician or, if they are to perform the calibrationprocedure themselves, they must have special training. Moreover, in thenormal course of use, targets and their associated clamps tend to changetheir relative geometry (e.g., if a clamp is dropped). While the clampsand targets may still be usable, this change in relative geometry is notreflected in the original system calibration, disadvantageouslyresulting in a degradation of alignment accuracy over time.

A need exists for a methodology and apparatus to determine the wheelaxis of rotation and wheel spindle point that does not requireadditional time to be taken to lift the vehicle and perform an extraprocess otherwise unnecessary for a typical alignment. A need alsoexists for a methodology and apparatus that can adjust for normal wearand tear of wheel target assemblies, to maintain alignment accuracy.Further, a need exists to minimize the cost of wheel clamps by removingthe need for self-centering capability.

SUMMARY

The disclosed system and methodology determines the wheel axis ofrotation and wheel spindle point every time an alignment is performed,by rolling the vehicle wheels and tracking the motion of the targetsattached to the wheels. The disclosed procedure can be performed at thesame time as a conventional rolling runout compensation procedure, whichis part of the standard wheel alignment process flow, and must beperformed near the beginning of an alignment procedure in any event.Also, the present disclosure enables calculation of the wheel spindlepoint and axis of rotation regardless of where the target is radiallylocated on the wheel, thereby eliminating the need for a self-centeringwheel clamp.

More particularly, this disclosure discusses the determination of wheelalignment angles from target pose measurements made when a wheel rollswithout slipping. A target placed at a radius between the axle of thewheel and the wheel circumference is tracked by a camera system.Specifically, the origin and the orientation of the target are tracked.Under the ideal circumstances of 2-D motion with no sliding, thetrajectory of the target origin traces the path of a curve known as acurtate cycloid as the wheel rolls. The angle of rotation of the wheelis determined from the changing pose of the target.

The virtual wheel spindle point can be computed from the motion of thetarget origin while the wheel rotates. There is an analytic solution tothe problem of computing the motion of the virtual wheel spindle pointwhen three target coordinates and poses are known with no measurementerror. The equation of the path taken by the target can be determined bymaking measurements of the target coordinates and pose, and fitting amodel to the data to determine the equation's parameters. The path ofthe virtual wheel spindle point is computed from the equation'sparameters.

One or more embodiments include a wheel alignment method for a vehicle,comprising affixing a target to a wheel of the vehicle, and providing acamera for viewing the target and capturing image data of the target.The vehicle is rolled while the wheel is on a substantially flat surfacesuch that the wheel and target rotate a number of degrees, while thecamera captures the image data of the target. The wheel axis of rotationis calculated along with a wheel spindle point based at least in part onthe captured image data. The wheel spindle point and the wheel axis ofrotation are used to compute an alignment parameter for the vehicle.

Embodiments further include a vehicle wheel alignment system comprisinga target fixedly attachable to a wheel of the vehicle; a camera forviewing the target and capturing image data of the target; and a dataprocessor. The data processor is adapted to receive the image data fromthe camera, and determine a vector pointing from the target origin to awheel spindle point based at least in part on the image data of thetarget captured, when the vehicle is rolled while the wheel is on asubstantially flat surface such that the wheel and target rotate anumber of degrees. The data processor is further adapted to calculate analignment parameter for the vehicle based at least in part on the wheelaxis of rotation and the coordinates of the wheel spindle point.

Embodiments also comprise a non-transitory computer readable mediumhaving instructions stored thereon that, when executed by a processor ofa vehicle wheel alignment system, cause the processor to determine analignment parameter for the vehicle. The alignment system has a targetfixedly attachable to a wheel of the vehicle and a camera for viewingthe target and capturing image data of the target. The determinationcomprises receiving the image data from the camera, determining thewheel axis of rotation and the coordinates of the wheel spindle point,based at least in part on the image data of the target captured when thevehicle is rolled while the wheel is on a substantially flat surfacesuch that the wheel and target rotate a number of degrees, andcalculating the alignment parameter for the vehicle based at least inpart on the wheel axis of rotation and the coordinates of the wheelspindle point.

Objects and advantages of embodiments of the disclosed subject matterwill become apparent from the following description when considered inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will hereinafter be described in detail below with referenceto the accompanying drawings, wherein like reference numerals representlike elements. The accompanying drawings have not necessarily been drawnto scale. Where applicable, some features may not be illustrated toassist in the description of underlying features.

FIG. 1 is a perspective view of a vehicle with a clamp/target assemblyattached, illustrating the virtual wheel spindle point, the wheelspindle point and wheel axis of rotation.

FIG. 2 is a diagram illustrating an example of how the coordinates of avirtual wheel spindle point in the plane of motion of the target originare computed when the wheel is free to rotate according to variousembodiments.

FIG. 3 is a diagram illustrating the path of a target when a vehiclewheel to which the target is attached is rolling.

FIG. 4 is a diagram describing the geometry of a rolling wheel with atarget attached, including parameters used in an exemplary derivation ofthe initial virtual wheel spindle point coordinates according to variousembodiments.

FIGS. 5A-5B are graphs showing rotation of 2-D target pose data into theY-Z plane during preprocessing according to various embodiments.

FIGS. 6A-6D are graphs showing fitting iterations as parameters areadjusted in a nonlinear least squares fit calculation according tovarious embodiments.

FIG. 7 is a graph showing measured coordinates of the target origin andvirtual wheel spindle point coordinates according to variousembodiments.

FIG. 8 is a graph showing an improved agreement between the virtualwheel spindle point coordinates determined by fitting coordinate data tothe virtual wheel spindle point coordinates computed according tovarious embodiments.

FIGS. 9A-9B are graphs showing outlying data points detected afterfitting a curtate cycloid to measured data according to variousembodiments.

FIG. 10 is a schematic top plan view of a self-calibrating wheelalignment system with which the disclosed system and methodology can beimplemented.

FIG. 11 is a schematic top plan view of a hybrid wheel alignment systemwith which the disclosed system and methodology can be implemented.

DETAILED DESCRIPTION

It should be understood that the principles described herein are notlimited in application to the details of construction or the arrangementof components set forth in the following description or illustrated inthe following drawings. The principles can be embodied in otherembodiments and can be practiced or carried out in various ways. Also,it is to be understood that the phraseology and terminology used hereinis for the purpose of description and should not be regarded aslimiting.

Disclosed herein are methods and systems for wheel axis vectorcalculations. FIG. 10 is a schematic top plan view of certain elementsof a computer-aided, 3D motor vehicle wheel alignment system(“aligner”), such as disclosed in U.S. Pat. No. 6,968,282 discussedherein above. This aligner has elements in common with the presentlydisclosed aligner, and can be used to implement the disclosedtechniques. In particular, the aligner of FIG. 10 comprises a leftcamera module 2 and a right camera module 4 that are used to alignwheels of a motor vehicle. The terms “left” and “right” are used forconvenience, and are not intended to require a particular element to belocated in a particular location or relationship with respect to anotherelement.

Arrow 30 of FIG. 10 schematically represents a motor vehicle undergoingalignment. The vehicle includes left and right front wheels 22L, 22R andleft and right rear wheels 24L, 24R. An alignment target 80 a, 80 b, 80c, 80 d is secured to each of the wheels 22L, 24L, 22R, 24R,respectively. Each alignment target generally comprises a plate 82 onwhich target information is imprinted and a clamping mechanism 88 forsecuring the target to a wheel. A left camera module 2 comprises leftalignment camera 10L. Left alignment camera 10L faces the vehicle andviews the left side targets 80 a, 80 b along axis 42. Right cameramodule 4 comprises a right camera 10R that faces the vehicle and viewsthe right side targets 80 c, 80 d along axis 44. Left camera module 2also includes a calibration camera 20 mounted perpendicularly to camera10L via a bracket 12. Calibration camera 20 views a calibration target16 attached to right camera module 4 via bracket 14 along axis 46, todetermine the positions of alignment cameras 10L, 10R relative to eachother. Each camera 10L, 10R, 20 has an illumination source 62, 64, 66.

The disclosed aligner further comprises a data processor (not shown),such as a conventional personal computer (PC), having software withinstructions to cause the data processor to perform the calculationsdescribed herein electronically.

The method and apparatus described herein is also applicable for usewith a hybrid aligner system as described in U.S. Pat. No. 7,313,869,which is hereby incorporated by reference in its entirety, and itscontinuation patents. FIG. 11 shows a schematic representation of anexemplary hybrid aligner system useable with the presently disclosedmethod and apparatus, including a pair of passive targets 21 and 23mounted on respective wheels 22 and 24 of the vehicle, which are frontsteering wheels in this first example. A pair of active sensing heads 25and 27 are adapted for mounting in association with other respectivewheels 26 and 28 of the vehicle, in this case the rear wheels. Eachactive sensing head includes a camera 29 or 31 for producing 2D imagedata, which is expected to include an image of one of the targets 21, 23when the various heads are mounted to the respective wheels of thevehicle. The system also uses two conventional (1D) angle sensors 33 and35 to measure the relative angles of the active sensing heads 25 and 27in the toe plane, and a pair of tilt sensors 37, 39 to measure tilt,typically camber and pitch, of heads 25, 27.

Definitions

Target Coordinate System: The coordinate system defined by the geometryof a target.

Target Origin: The mathematical point defined to be the origin of thetarget coordinate system.

Wheel Axis of Rotation: The axis about which the wheel rotates. Alsoknown as the wheel spindle axis.

Wheel Rim Plane: The plane defined by the wheel rim outer surface.

Virtual Wheel Spindle Point: point along the axis of rotation of thewheel around which the target origin rotates.

Wheel Spindle Point: point at which the axis of rotation of the wheelintersects the wheel rim plane.

Target Radius: distance between the target origin and the virtual wheelspindle point.

Camera tilt angle: tilt angle of the camera relative to the direction ofmotion of the wheel spindle.

Starting roll angle: angular location on the wheel where the targetorigin is located when the roll starts.

Jacked Wheel Spindle Calibration: the process for or result of computingthe wheel axis of rotation and virtual wheel spindle point frommeasurements made while the wheel is raised so it can rotate freelywithout linear motion.

Rolling Wheel Spindle Calibration: the process for or result ofcomputing the wheel axis of rotation and virtual wheel spindle pointfrom measurements made while the wheel is rolling.

The disclosed rolling wheel spindle calibration techniques provideseveral distinct advantages over the conventional jacked wheel spindlecalibration procedure. One advantage is that rolling wheel spindlecalibration is an “online” rather than an “offline” process. Rollingwheel spindle calibration is performed every time rolling runoutcompensation is performed, which is part of the standard wheel alignmentprocess flow. Unlike jacked wheel spindle calibration, there is nospecial procedure that must be followed and there is no special trainingthe end-user must have to perform this system calibration. As a result,a trained field service representative with custom calibration equipmentis not needed to perform high accuracy system calibrations. This savesthe end user time and money.

Another advantage of being an online process is that true wheel spindlecalibration changes over time. In the normal course of use, targets andclamps tend to change their relative geometry (e.g., when clamps areaccidentally dropped). There is nothing wrong with this change inrelative geometry; all that matters is that the relative geometry isaccurately reflected in the wheel spindle calibration. As an onlinemeasurement, rolling wheel spindle calibration provides the mostup-to-date measurement of the wheel spindle point coordinates and wheelaxis of rotation orientation.

Another advantage of rolling wheel spindle calibration is experiencedwhen employing vehicle-centric wheel alignment coordinate systems. Inconventional vehicle-centric coordinate systems, a coordinate system isconstructed based upon measurements of a vehicle under examination,typically, using the centers of the vehicle's wheel rims. When thedisclosed rolling wheel spindle calibration is employed, one does notassume a fixed spatial relationship between the target and the wheel rimcenters. The centers of the wheel rims are computed as part of theprocess. As a result, the target can be placed at any relative radialposition with respect to the wheel axis. In other words, the target canbe affixed to the wheel such that the target origin is disposedsubstantially on the axis of rotation of the wheel, or such that thetarget origin is offset from the wheel axis of rotation. The disclosedrolling wheel spindle calibration techniques thus provide freedom in thetype of targets used.

Overview

The purpose of a wheel spindle calibration measurement is to determinethe location of the wheel spindle point relative to the target for allpositions and orientations of the wheel to which the target is attached.The wheel spindle point is a point at the intersection of the axis ofrotation of the wheel and the plane defined by the outward face of therim of the wheel. The origin of the target coordinate system istypically referred to as the target origin. Determining the location ofthe wheel spindle point along with the direction of the wheel axis ofrotation is an integral part of determining wheel and frame alignment,as those of skill in the art will appreciate.

The measureable quantity for any position of the wheel is the targetorigin and the orientation of its pose. The wheel axis of rotation iscomputed from the change to the orientation of the pose of the target asthe wheel is rotated. The coordinates of the wheel spindle point in thetarget coordinate system is invariant as the wheel is rotated.

The conventional procedure for determining the wheel spindle point andwheel axis of rotation is to lift the vehicle so the wheels are free torotate. Each wheel is then rotated to at least two positions whileobserving the target attached to the wheel and measuring the targetpose. Measurement of the target pose along with the coordinates of thetarget origin at the two positions allows for the calculation of therotation angle between the target poses, the vector defining the wheelaxis of rotation, the target radius, and the virtual wheel spindlepoint. The geometry is shown in FIG. 2, wherein:

-   -   X: ½ the chord length between the measured points    -   θ: The angle of rotation of the target    -   P₁, P₂: Measured coordinated of target centroid    -   C: center of circle with coordinated (X₀, Y₀)

The plane defined by the target origin as it rotates around the wheelaxis of rotation is parallel to the plane defined by the face of thewheel rim in which the wheel spindle point is located. The distancebetween these two planes is called the target offset distance and isdetermined by the clamp geometry. This distance is used to compute thecoordinates of the wheel spindle point relative to the target origin.

Raising the vehicle, rotating the wheels while making measurements, andlowering the vehicle are error prone, time consuming, labor intensiveand expensive processes that users seek to avoid. Using the conventionalprocedure described immediately above, lifting the vehicle is requiredevery time the combined system of a target and its clamp need to becalibrated. Systems using self-centering clamps are used in combinationwith targets and calibrated once for use on subsequent vehicles. Theimportant feature of self-centering clamps is they can be placed onwheels such that the relative target to virtual wheel spindle pointtranslation is fixed. But self-centering clamps impose undesirable size,appearance, and cost constraints.

Both the cost of lifting the vehicle and the cost of self-centeringclamps makes it desirable to develop an alternative method to performwheel spindle calibration without needing to raise the vehicle. It isadvantageous to compute the wheel spindle point and wheel axis ofrotation while the vehicle wheels roll without slipping on the ground.This is already part of the process for computing wheel alignment (e.g.,conventional rolling runout compensation) and does not require a specialcalibration step in the process. An advantage of the disclosed rollingwheel spindle calibration is that the clamp/target system is notrequired to have a fixed self-centering geometry. The requirement forcalibrating such a system with each use means only a simple calibrationprocedure is needed.

Calibrating a Raised Wheel

When the wheel is raised and rotated, a target located at a radialdistance from the wheel axis of rotation (virtual wheel spindle point)traces out a circle. The radius and location of the virtual wheelspindle point can be computed from two target coordinates and the angleof rotation or central angle between them. This is illustrated in FIG. 2as follows:

1. The wheel axis of rotation is normal to the plane in which the twomeasured points P₁, P₂ and the center of rotation lie.

2. The wheel axis of rotation is on the perpendicular bisector b of thechord between the two measured points P₁, P₂.

3. The length (2×) of the chord is known.

4. The perpendicular bisector b of the chord bisects the known angle θbetween the two measured points P₁, P₂.

First, solve for the radius R in terms of θ and x. Then solve for theintersection of the two circles with radius R centered at P₁ and P₂.There are two solutions for the center of the circle, but only onesolution falls on the correct side of the line between P₁ and P₂.Rolling Wheel Spindle Calibration

Calibration of a rolling wheel spindle according to the presentdisclosure will now be described. When the wheel is rolling withoutslipping while in contact with the ground, a target traces out a curtatecycloid. As shown in FIG. 3, the path 300 of the target origin t denotesa curtate cycloid. For practical reasons, only a small portion of thepath 300; e.g., a 90 degree range of motion 310, is measured. Themeasurement range 310 is limited because the camera 320 always needs toview the face of the target (not shown, but can be similar to target120). The center of rotation of the wheel 330 and its direction ofmotion is not a measured feature. The measurement of the position andorientation of the target use single perspective n-point poseestimation. At each target position, both the coordinates andorientation of the target is computed. The direction of the wheel axisof rotation around which rotation occurs is computed from the change inpose.

Measurements made in a two dimensional plane consist of three coordinatemeasurements with a pose measurement made at each position. From thesemeasurements the following parameters are computed:

1. Diameter of wheel 330;

2. Target radius;

3. Starting position of wheel 330 relative to the camera 320 (X, Y, Zcoordinates);

4. Rotational angle of the target while attached to the wheel 330 at itsstarting position;

5. The camera's tilt angle A or direction of travel of the wheel 330relative to horizontal as defined by the camera axis.

The parameters of a curtate cycloid in a plane are exactly solvable fromthree measured points and the angular differences between them. FIG. 4shows the geometry of a rolling wheel with a target attached at radiusr_(t), and describes a derivation of the initial wheel spindlecoordinate, wherein:C _(N) =W _(O) +r _(ω)θ_(ON) ω+R _(ON)( C _(O) −W _(O))

-   -   r_(t): target radius    -   R_(ON): rotation matrix rotates (C _(O)−W _(O)) into (C _(N)−W        _(N))    -   r_(ω)θ_(ON): linear travel of wheel    -   ω: vector specifying direction of linear travel    -   I: identity matrix

A bar over a variable signifies the variable is a vector. The equation

$\begin{matrix}\left. {{\overset{\_}{W}}_{0} = {{\left( {I - R_{01} - {\frac{\theta_{01}}{\theta_{02}}\left( {I - R_{02}} \right)}} \right)^{- 1}\left( {{\overset{\_}{C}}_{1} - {R_{01}{\overset{\_}{C}}_{0}}} \right)} - {\frac{\theta_{01}}{\theta_{02}}\left( {{\overset{\_}{C}}_{2} - {R_{02}{\overset{\_}{C}}_{0}}} \right)}}} \right) & (1)\end{matrix}$computes the coordinates of the initial wheel spindle points as afunction of the coordinates of the target origin and rotation angle. Thewheel spindle point coordinates for every position of the target canalso be computed given the initial wheel spindle point coordinate, thedirection of travel, and the rotation angle.

It should be noted the disclosed rolling wheel spindle calibrationtechnique can also handle the case of a raised wheel. Any linear travelof the wheel is defined by the term r_(ω)θ_(ON). When this term is setto zero in the implementing software, all of the data points lie on thecircumference of a circle. The software then proceeds to compute thestationary wheel spindle point W_(O) and the target radius.

Data Pre-Processing

The measured data points are sorted in order of increasing Z coordinate.As a result, it does not matter whether a wheel is rolled forward orbackward in the disclosed techniques. The order of the measured angulardifferences in the changing target pose is defined by the sorting. Withregards to the 3-pt formula, the initial wheel spindle point coordinateW_(O) is closest to the camera. The simulated data generated during thenon-linear least squares search described herein below uses the angulardifferences extracted from the measured data.

Estimation of rolling parameters of a wheel is essentially a2-dimensional problem with small deviations of the motion of the targetorigin from a 2-dimensional plane because of noise and a small helicalmotion because of vehicle toe. The trajectory of the wheel can bethought of as having roll, pitch, and yaw relative to the camera. Theroll and yaw parameters can be computed in advance, leaving an unknownpitch in the data. The pitch corresponds to any downward view of thecamera relative to the linear motion of the wheel, and in this documentis referred to as the camera tilt angle (denoted by reference characterA in FIG. 3). Roll corresponds to camera rotation, and yaw anyleft-right orientation of the camera relative to the linear motion ofthe wheel.

Roll and yaw can be determined from the axis of rotation of the targetmeasured from pose to pose. FIGS. 5A-B show the rotation of the datainto the Y-Z plane during preprocessing. The Y-Z plane is defined by thecamera coordinate system. The data in FIG. 5A is translated and rotatedto lie in the Y-Z plane for processing in FIG. 5B. Pre-processingremoves some of the computational burden of the problem for both athree-point fit and a non-linear fit.

Nonlinear Least Squares Search for Parameters

For practical reasons, more than three pose measurements may be neededto perform the disclosed rolling wheel spindle calibration. As a skilledartisan would understand, measurement noise can affect image processing,the vehicle may not move in a straight line (the wheels may be turned),the platform the vehicle rolls on may include bumps, and/or the platformthe vehicle rolls on may slide so the wheels may not undergo purerotation. Alternatively, the wheel may bump slightly because of a gapbetween the plate and the platform. In addition, the range of motion ofthe vehicle may be limited by mechanical constraints. One result ofthese complexities is that the three pose solution may be prone toerror. The disclosed techniques therefore include more data points, andfitting the parameterized curve of a curtate cycloid to the measureddata. In this way, the data can be processed to detect and compensatefor unexpected motion and other complexities.

According to certain embodiments, if more than three measured points areacquired during the vehicle roll, a well-known least squares fittingapproach is taken to process the data (with only three points, thesolution is exact). The following can disadvantageously affect results:

1. As the wheel rolls from one position to the next the wheel can turnslightly. If there are more than three points, the measured points maynot lie in a plane. Also, the direction of the wheel axis of rotationwill vary.

2. As the wheel rolls from one position to the next it may encounterbumps or slide without rolling.

3. The wheel may not be perfectly round, and it is not understood howthe wheel deformation affects the motion of the target.

4. Tire treads may induce variation in the motion of the target.

5. There may be errors in the pose angle measurements of the targets,generating errors in the estimated angular rotation of the wheel.

For these reasons, a numerical optimization method is implemented bythis disclosure to estimate the wheel parameters and wheel spindlepositions during rolling. The numerical optimization method minimizesthe error between the measured data and simulated data by adjustingmodel parameters. The model parameters include wheel diameter, targetradius, the direction of linear motion of the wheel relative to thecamera axis, and the starting position of the wheel relative to thecamera. The model parameters are then used to compute the locations ofthe wheel spindle point as the wheel rolls. The wheel spindle points andwheel axis of rotation are then computed using the measured posecoordinates and orientation.

In some embodiments, the well-known Nelder-Mead optimization method isused to determine the model parameters by minimizing the aggregate RMSerror, defined as the difference between the measured target coordinatesand the simulated model coordinates. The method performs a nonlinearleast squares fit of the simulated data to the measured data. FIGS. 6Athrough 6D show four iterations of the fitting process as the error isminimized, wherein the measured data is denoted by reference numeral 600and the coordinates generated by the fitting function are denoted byreference numerals 610-640. The parameters which can be adjusted includethe wheel diameter, the target radius, closest position of the wheelduring its roll, orientation of the target at its closest position, thecamera's orientation relative to the direction of travel.

The parameters which are varied during the fitting process are:

1. Wheel Spindle Y-coordinate.

2. Wheel Spindle Z-coordinate.

3. The direction of the wheel is moving relative to the camera axis(i.e., camera tilt angle).

4. Angular position of the target at the start of the roll.

5. The radius of the target origin relative to the wheel axis ofrotation.

6. The wheel diameter.

The fitting of a curtate cycloid to the measured data is sensitive tonoise. The fitting algorithm always converges and provides the correctwheel spindle coordinates, wheel diameter and radius for simulated datawhere the added noise is random. With real data, the parameters willadjust to minimize the aggregate error, but the result can includeerrors in the parameters. An error will appear as a shift in thelocation and direction of the wheel spindle coordinates relative to thetarget coordinates. This shift is seen in FIG. 7 as a difference betweenthe virtual wheel spindle point coordinates 700 computed from the fit,and the virtual wheel spindle point coordinates 710 determined by thecalibrated target/clamp system (i.e., based on clamp calibration duringrolling).

FIG. 8 shows improved agreement between the virtual wheel spindle point800 determined by fitting the coordinate data, and the reference virtualwheel spindle point 810 determined when using a self-centering clamp. Inthis embodiment, higher order terms were added to the model to accountfor motion of the wheel which was not exactly proportional to itsrotational motion. These additional terms improved the fitting error andthe error in the wheel spindle point coordinates. Fitting the targetorigin coordinates to a model may not be sufficiently robust in anunconstrained environment with sliding and rotating platforms.

One solution is to remove degrees of freedom from the measurement. Onemethod is to use a clamp which, while not self-centering, positions thetarget origin close to the wheel axis of rotation.

Another method is to augment the target measurements with anothermeasurement that defines the direction of wheel axis of rotation travel.An example is a target pattern visible on the floor so the pose of thefloor was known. Other examples include a marker attached to the vehiclebody while it is moved, or a signal from an electronic level attached tothe target. This additional measurement removes the camera tilt angle asan unknown parameter.

Alternative Methods for Computing Rolling Wheel Spindle Calibration

To compute rolling wheel spindle calibration, one need not use theNelder-Mead simplex algorithm described in the embodiment above. Thoseof skill in the art will appreciate that one could compute rolling wheelspindle calibration via analytical parameter models including gradientdescent, Levenberg-Marquardt, and other iterative nonlinear leastsquares methods. The class of algorithms collectively known as “gridsearch” algorithms constitutes another set of usable alternatives. Gridsearch algorithms are non-parametric parameter estimation algorithmstypically employed where the optimization process is not guaranteed tooccur in a purely convex space. These are several alternative methodswhich could be employed in other embodiments in lieu of the Nelder-Meadsimplex algorithm.

Removal of Outliers

The trajectory of the curtate cycloid traced out by target origin is asmooth arc. A bump in the wheel motion may be detected as an outlier inthe data. In certain embodiments illustrated by FIGS. 9A-9B, outlierdetection is accomplished by performing an initial fit of a curtatecycloid to the data (FIG. 9A). If the aggregate error is large, adecision is made to remove the data point 910 with the largest error anditerate the process until the error is small (see, fit 920 of FIG. 9B).This process of generating a fit to the data and removing outliers canbe run repeatedly until the aggregate error falls below a threshold andthere are sufficient remaining points.

As pointed out previously, the standard required rolling runoutcompensation procedure can be performed at the same time as thedisclosed wheel spindle calibration, based at least in part on the imagedata captured when the vehicle is rolled to determine the wheel spindlepoint coordinates and wheel axis of rotation direction vector. Anexemplary technique for determining rolling runout is described inabove-discussed U.S. Pat. No. 5,535,522 at col. 12:5-30. Those of skillin the art will appreciate that other conventional rolling runouttechniques can be employed. The wheel spindle point coordinates andwheel axis of rotation direction vector and the rolling runoutcalculation can both be used to calculate an alignment parameter for thevehicle; e.g., toe, camber, etc. in a conventional manner.

Embodiments of a method, system and computer program product for rollingwheel spindle determination may be implemented on a general-purposecomputer, a special-purpose computer, a programmed microprocessor ormicrocontroller and peripheral integrated circuit element, an ASIC orother integrated circuit, a digital signal processor, a hardwiredelectronic or logic circuit such as a discrete element circuit, aprogrammed logic device such as a PLD, PLA, FPGA, PAL, or the like. Ingeneral, any process capable of implementing the functions or stepsdescribed herein can be used to implement embodiments of the method,system, or computer program product for rolling wheel spindledetermination.

Furthermore, embodiments of the disclosed method, system, and computerprogram product for rolling wheel spindle determination may be readilyimplemented, fully or partially, in software using, for example, objector object-oriented software development environments that provideportable source code that can be used on a variety of computerplatforms. Alternatively, embodiments of the disclosed method, system,and computer program product for rolling wheel spindle determination canbe implemented partially or fully in hardware using, for example,standard logic circuits or a VLSI design. Other hardware or software canbe used to implement embodiments depending on the speed and/orefficiency requirements of the systems, the particular function, and/ora particular software or hardware system, microprocessor, ormicrocomputer system being utilized. Embodiments of the method, system,and computer program product for rolling wheel spindle determination canbe implemented in hardware and/or software using any known or laterdeveloped systems or structures, devices and/or software by those ofordinary skill in the applicable art from the functional descriptionprovided herein and with a general basic knowledge of the computerand/or wheel alignment arts.

It is, therefore, apparent that there is provided in accordance with thepresent invention, a method, system, and computer program product forperforming a rolling wheel spindle determination. While this inventionhas been described in conjunction with a number of embodiments, it isevident that many alternatives, modifications and variations would be orare apparent to those of ordinary skill in the applicable arts.Accordingly, applicants intend to embrace all such alternatives,modifications, equivalents and variations that are within the spirit andscope of this invention.

What is claimed is:
 1. A method comprising: affixing a target to a wheelof the vehicle; providing a camera for viewing the target and capturingimage data of the target; rolling the vehicle such that the wheel andtarget rotate while the camera captures the image data of the target;calculating a wheel axis of rotation based at least in part on thecaptured image data; calculating a virtual wheel spindle point in theplane of motion of the target origin around which the target originrevolves, based at least in part on the captured image data; and usingthe virtual wheel spindle point and wheel axis of rotation to calculatea direction of travel of the wheel.
 2. The method of claim 1, comprisingcalculating a wheel spindle point based at least in part on the capturedimage data and using the wheel spindle point to calculate an alignmentparameter for the vehicle.
 3. The method of claim 1, comprisingcalculating a rolling runout of the wheel based at least in part on thecaptured image data, and using the rolling runout calculation tocalculate the alignment parameter for the vehicle.
 4. The method ofclaim 1, comprising calculating the virtual wheel spindle point using aniterative nonlinear least squares technique.
 5. The method of claim 4,wherein the iterative nonlinear least squares technique comprises one ofa Nelder-Mead simplex algorithm, a Levenberg-Marquardt algorithm, and agradient descent algorithm.
 6. The method of claim 1, comprisingcalculating the virtual wheel spindle point using a grid searchalgorithm.
 7. The method of claim 1, comprising affixing the target tothe wheel such that the target origin is offset from the wheel axis ofrotation.
 8. The method of claim 1, comprising affixing the target tothe wheel such that the target origin is disposed substantially on thewheel axis of rotation.
 9. A system comprising: a target fixedlyattachable to a wheel of the vehicle; a camera for viewing the targetand capturing image data of the target; and a data processor adapted to:receive the image data from the camera, determine a wheel axis ofrotation based at least in part on the image data of the target capturedwhen the vehicle is rolled such that the wheel and target rotate;determine a virtual wheel spindle point, based at least in part on theimage data of the target captured when the vehicle is rolled, andcalculate a direction of travel of the wheel based at least in part onthe wheel axis of rotation and the virtual wheel spindle point.
 10. Thesystem of claim 9, comprising calculating a wheel spindle point based atleast in part on the captured image data and using the wheel spindlepoint to calculate an alignment parameter for the vehicle.
 11. Thesystem of claim 9, wherein the data processor is adapted to calculate arolling runout of the wheel based at least in part on the captured imagedata, and calculate an alignment parameter for the vehicle based atleast in part on the rolling runout.
 12. The system of claim 9, whereinthe data processor is adapted to calculate the virtual wheel spindlepoint coordinates using an iterative nonlinear least squares technique.13. The system of claim 11, wherein the iterative nonlinear leastsquares technique comprises one of a Nelder-Mead simplex algorithm, aLevenberg-Marquardt algorithm, and a gradient descent algorithm.
 14. Thesystem of claim 9, wherein the data processor is adapted to calculatecoordinates of the virtual wheel spindle point using a grid searchalgorithm.
 15. The system of claim 9, comprising a clamp for affixingthe target to the wheel such that the target origin is offset from thewheel axis of rotation.
 16. The system of claim 9, comprising a clampfor affixing the target to the wheel such that the target origin isdisposed substantially on the wheel axis of rotation.
 17. The system ofclaim 9, wherein the data processor is adapted to compare coordinates ofthe calculated virtual wheel spindle point to predetermined referencevirtual wheel spindle coordinates, and inform a user when the calculatedvirtual wheel spindle coordinates are outside the range of referencevirtual wheel spindle coordinates.